As painful as this may sound, I recommend using rubbing alcohol to really eliminate all the bacteria in the cuts. Just pour it on, endure the pain for a few seconds. Owwie. Then let it air-dry and pour hydrogen peroxide on them. Depending on where the cuts are, you should find a way to wrap a gauze pad around them, as gauze is absorbant and will remove any weeping/moisture that attracts bacteria. I went through this every time I slid in softball.
Silly team. Shorts were part of our uniform! It's supposed to be PANTS!!